Problem: Rewrite as a simplified fraction. ${0.12\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 128.8888...\\ 100x &= 12.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 116}$ ${x = \dfrac{116}{900}} $ ${x = \dfrac{29}{225}} $